Arbitrary pure single-qubit states on the \(xz\)  plane of the Bloch Sphere can be cloned with fidelity \(f := (1/2 + 1/2\sqrt{2}) \approx 0.85\)  [1]}. Since every ciphertext lies on the \(xz\)  plane in conjugate encryption, a cloning adversary (for each qubit) clone the ciphertext with fidelity \(f\) . In phase 2, both \(\mathcal {B}\)  and \(\mathcal {C}\)  will decrypt their register, hence each having fidelity \(f\)  to the message \(|m\rangle \langle m|\) . By union bound, this implies that they both output \(m\)  with probability at least \((2f-1)^n \approx 0.7^n\) . In the single-bit message case, this means that the scheme of [2]} can be violated by an adversary with probability 0.7. For details of these upper-lower bounds, see REF  and REF .
